Marcin Kucharczyk

GF(q) LDPC decoder design for FPGA implementation

The concept of Low Density Parity Check (LDPC) coding over Galois Fields GF (q = 2p) is a generalization of the industry standard binary LDPC coding. The performance for short block length codes is significantly higher for non-binary codes (over higher order GF fields), but on the other hand, the decoding complexity is increased. Therefore the hardware implementation of a decoder is still a challenging task. Most of the few implementations known from the literature use multiplierless computing units. In this article we present a different approach that does not exclude multiplier blocks from the decoder module. This approach is specifically intended for FPGA (Field Programmable Gate Array) implementation. We propose the decoding algorithm formulation that uses multiplications in the computation step of the Check Nodes and summations performed in the Bit Nodes. The main reason is to enable mapping a part of the algorithm to the multiplier cores available in the FPGA devices. In the article we present the decoder structure that has been developed and the construction of its building blocks. We also provide synthesis results for the Xilinx FPGAs and simulation results for a simple BPSK (Binary Phase Shift Keying) modulation model over AWGN (Additive White Gaussian Noise) channel.

Blind Signatures in Electronic Voting Systems

Electronic voting systems are created to facilitate the election, accelerate voting and counting votes and increase turnout for the election. The main problems of the electronic systems are related with the assurance of system security (cryptographic security and protection against frauds) and a guarantee that the voters are anonymous. The authorization of voters and the anonymity of them seem to be contradictory, but it is possible to create such a system where the both requirements are met. Some solutions, the most common e-voting systems, are presented in the paper. These models are adjusted to the demands and implemented in the polls system for quality of teaching evaluation where anonymity is very important. The blind signature protocol, model directed to user’s anonymity, is a very good solution of the authorization and anonymity problem in the polls system with remote access only, as it was described in the paper.

Transmission over UWB Channels with OFDM System using LDPC Coding

Hostile wireless environment requires use of sophisticated signal processing methods. The paper concerns on Ultra Wideband (UWB) transmission over Personal Area Networks (PAN) including MB-OFDM specification of physical layer. In presented work the transmission system with OFDM modulation was connected with LDPC encoder/decoder. Additionally the frame and bit error rate (FER and BER) of the system was decreased using results from the LDPC decoder in a kind of turbo equalization algorithm for better channel estimation. Computational block using evolutionary strategy, from genetic algorithms family, was also used in presented system. It was placed after SPA (Sum-Product Algorithm) decoder and is conditionally turned on in the decoding process. The result is increased effectiveness of the whole system, especially lower FER. The system was tested with two types of LDPC codes, depending on type of parity check matrices: randomly generated and constructed deterministically, optimized for practical decoder architecture implemented in the FPGA device.

OFDM Transmission with Non-binary LDPC Coding in Wireless Networks

High-quality information exchange between upper layers of the communication network (e.g. TCP, IP layers) requires reliable connection of communicating devices on the physical layer. Any non-corrected errors at this level force the upper layers to perform proper action to recover transmitted information. It reduces data throughput and increases delay to unacceptable level for some services. Among physical media, wireless one is the most hostile environment, due to its unpredictable behavior. In that case, OFDM (Orthogonal Frequency Division Multiplex) modulation and LDPC (Low Density Parity Check) error correction codes appear the best choice to provide high transmission quality on the physical layer. This paper presents the results of the authors’ simulation of a LDPC-coded OFDM system with particular emphasis on codes over high order Galois fields (non-binary) which are not commercialized yet.

Modified OMP Algorithm for Compressible Channel Impulse Response Estimation.

Wireless communication link at the physical layer can be described as a signal transmission over multiple propagation paths which are different in the gain and the delay. But in reality there are only a few significant paths responsible for the most signal energy transmission between transmitter and receiver. Such a sparse nature of the propagation environment promotes the use of the compressed sensing methods for channel impulse response estimation in the receiver. Unfortunately, a typical band-limited transmission violates the strict channel sparsity making the impulse response reconstruction more complex. The paper presents an analysis of channel impulse response estimation with the Orthogonal Matching Pursuit algorithm. A modification of the classical OMP method is proposed in order to improve both the channel estimation and the data transmission qualities in case of a weak condition of the impulse response sparsity. This proposition is numerically evaluated for the general case of the OFDM transmission over a sixth path urban channel model. The results are compared to the ones obtained for the strict sparse impulse response instance.

Partial parallel encoding and algorithmic construction of non-binary structured IRA codes

The non-binary (NB) Irregular Repeat Accumulate (IRA) codes, as a subclass of NB LDPC codes, potentially have an excellent error-correcting performance. They are also known to provide linear complexity of encoding, but the basic encoding method with the serial rate-1 accumulator significantly limits the encoder throughput. Then the objective of the research presented in this paper is to develop an encoding method providing significantly increased throughput of an NB-IRA encoder altogether with a flexible code construction methods for the structured (S-NB-IRA) codes eligible for the proposed encoding method. For this purpose, we reformulate the classic encoding algorithm to fit into the partial parallel encoder architecture. We propose the S-NB-IRA encoder block diagram and show that its estimated throughput is proportional to the submatrix size of the parity check matrix, which guarantees a wide complexity-throughput tradeoff. Then, in order to facilitate the S-NB-IRA coding systems design, we present a computer search algorithm for the construction of good S-NB-IRA codes. The algorithm aims at optimizing the code graph topology along with selecting an appropriate non-binary elements in the parity check matrix. Numerical results show that the constructed S-NB-IRA codes significantly outperform the binary IRA and S-IRA codes, while their performance is similar to the best unstructured NB-LDPC codes.

Column weights optimization for semi-regular nonbinary LDPC codes

The paper concerns Low Density Parity Check (LDPC) codes over nonbinary Galois Fields GF(q), that are a generalization of the industrial standard binary LDPC codes for forward error correction in communication and information systems. The semi-regular nonbinary LDPC codes can outperform their binary counterparts in the case of short to moderate code word lengths. The methods for the good code construction based on a computer search techniques are already well investigated. However, there is a lack of systematic results for optimal weight distribution of columns of parity check matrices for codes over different field order and different rate. In this article we present a Monte Carlo like algorithm for column weight optimization devoted to nonbinary semi-regular codes along with optimization results that facilitate the codes construction computer-based methods.

Simple Communication with FPGA Device over Ethernet Interface

Individual components of the communication system can be implemented in different environments on the stage of design and prototyping. Some of them are simulated in a high-level language environment, like matlab, and some are implemented in a target device, FPGA or signal processor, using evaluation boards. The verification of hardware implementation needs the communication interface sufficiently fast to transmit high amount of data. The Ethernet interface widely available on modern boards seems to be useful. The paper presents a set of modules, compiled as applications as well as implemented in FPGA, used to send data between PC and FPGA device over Ethernet omitting the TCP/IP protocol stack. The data are send and received by direct access to the Ethernet frames. Simple transmission protocol with acknowledgment was proposed to provide reliable data transmission.

Student’s Polls for Teaching Quality Evaluation as an Electronic Voting System

The problems of electronic voting (e-voting) systems are commonly discussed in case of general election. The main problems of e-voting are related with the system security and the user’s anonymity. System security is the problem of cryptographic security, user’s authorization, limited access and protection against frauds. The anonymity is another important issue, because a guarantee that the voters are anonymous is reflected in the reliability of casted votes. Authorization and anonymity seems to be contradictory but it possible to separate both procedures. The problems of polls for teaching quality evaluation are similar. The polls need to be available only for authorized students but they also need to be filled in anonymously. Three solutions of such a problem in remote voting system are discussed in the document.

Initialization strategies for prewhitened blind equalization

The paper presents theoretical considerations and simulation analysis of some modifications applied to the linear blind equalization procedure. The proposed idea of the equalizer order estimation together with modified equalizer structures improves their working flexibility, understood as initial automatic adjustment of the equalizer parameters in accordance with the unknown channel conditions. The results of the optimal whitening filtering performed prior to equalization procedure are the entry point to develop proposed solutions. Numerical experiments confirm that for the determined equalizer parameters, the assumed distortion level in the receiver output can be achieved. The analysis was done under the baud-spaced equalizer and single input single output (SISO) communication scheme.